To get it installed, the best solution I could come up with was to create the silverstripe-cache directory in root as normal, giving 777 permission and then to change line 725 in framework/dev/instal/install.php5
from - $ssTmp = "$sysTmp/silverstripe-cache";
to - $ssTmp = "/silverstripe-cache";
Not pretty but at least it got me up and running.
Friendly URLs appeared not to be working after install as I was redirected to an index.php? page but actually were, and all seems fine.
If SS3 does not reuire silverstripe-cache then why does the installation page tell me it requires write access to it?
Your "friendly urls not working" is an unrelated problem. You'll find a lot of existing help on that in this forum.